April 20, 2011

Imagine if someone at a dinner party casually announced, “I’m illiterate.” It would never happen, of course; the shame would be too great. But it’s not unusual to hear a successful adult say, “I can’t do math.” That’s because we think of math ability as something we’re born with, as if there’s a “math gene” that you either inherit or you don’t.

School experiences appear to bear this out. In every math class I’ve taken, there have been slow kids, average kids and whiz kids. It never occurred to me that this hierarchy might be avoidable. No doubt, math comes more easily to some people than to others. But the question is: Can we improve the methods we use to teach math in schools — so that everyone develops proficiency?

Looking at current math achievement levels in the United States, this goal might seem out of reach. But the experience of some educators in Canada and England, using a curriculum called Jump Math, suggests that we seriously underestimate the potential of most students and teachers.

“Almost every kid — and I mean virtually every kid — can learn math at a very high level, to the point where they could do university level math courses,” explains John Mighton, the founder of Jump Math, a nonprofit organization whose curriculum is in use in classrooms serving 65,000 children from grades one through eight, and by 20,000 children at home. “If you ask why that’s not happening, it’s because very early in school many kids get the idea that they’re not in the smart group, especially in math. We kind of force a choice on them: to decide that either they’re dumb or math is dumb.”

Children come into school with differences in background knowledge, confidence, ability to stay on task and, in the case of math, quickness. In school, those advantages can get multiplied rather than evened out. One reason, says Mighton, is that teaching methods are not aligned with what cognitive science tells us about the brain and how learning happens.

In particular, math teachers often fail to make sufficient allowances for the limitations of working memory and the fact that we all need extensive practice to gain mastery in just about anything. Children who struggle in math usually have difficulty remembering math facts, handling word problems and doing multi-step arithmetic (pdf). Despite the widespread support for “problem-based” or “discovery-based” learning, studies indicate that current teaching approaches underestimate the amount of explicit guidance, “scaffolding” and practice children need to consolidate new concepts. Asking children to make their own discoveries before they solidify the basics is like asking them to compose songs on guitar before they can form a C chord. ...

Take the example of positive and negative integers, which confuse many kids. Given a seemingly straightforward question like, “What is -7 + 5?”, many will end up guessing. One way to break it down, explains Mighton, would be to say: “Imagine you’re playing a game for money and you lost seven dollars and gained five. Don’t give me a number. Just tell me: Is that a good day or a bad day?”

Separating this step from the calculation makes it easier for kids to understand what the numbers mean. Teachers tell me that when they begin using Jump they are surprised to discover that what they were teaching as one step may contain as many as seven micro steps. Breaking things down this finely allows a teacher to identify the specific point at which a student may need help. “No step is too small to ignore,” Mighton says. “Math is like a ladder. If you miss a step, sometimes you can’t go on. And then you start losing your confidence and then the hierarchies develop. It’s all interconnected.”

In other words, the secret to better math education is to Have the slow kids go slower. Don't introduce the Pythagorean Theorem to everybody in second grade, as is common lately. Instead, make the not so bright kids chant their times tables until they're burned into their memories. Use educational tricks on the dumb kids like "Imagine you’re playing a game for money and you lost seven dollars and gained five. Don’t give me a number. Is that a good day or a bad day?" that would put smarter kids to sleep.

Of course, these methods would be disastrous for the smarter kids, so the bottom-line macro implication is: Track, track, track.

(A second order implication is that individual tutoring, which tends to work better than less labor-intensive ways of teaching math, should be handed off to computers that can customize each lesson and quiz for the individual student. On the other hand, notice that Steve Jobs's Apple products were heavily aimed at the educational market 30 years ago, but almost ignore schools today. Most educational software in 2011, sadly, comes from small firms that deserve to be small.)

Of course, all this subversive wisdom about not ignoring cognitive differences has to be phrased as being part of the Holy War on Charles Murray.

I suppose this kind of subterfuge is, on the whole, better than the current orthodoxy, which is to accelerate everybody in math to avoid the soft bigotry of low expectations, which leads to lots of kids who could have mastered arithmetic counting on their fingers as they fail algebra. Arithmetic really, really matters in real life: arithmetic skills are an important hurdle in determining who moves up from carpenter's helper to carpenter and from carpenter to contractor. But elementary and middle schools put less relative emphasis arithmetic today and more on "rigorous" math because Studies Have Shown that kids who aced Algebra I in 7th grade are more likely to graduate from college. (It might also be useful to teach more people how to Think About Statistics.)

Still, the need to lie all the time, especially about bell curves, means that practically nobody in the Education Biz ever learns any broadly applicable lessons even from success stories. How many readers of this story will figure out the real message? Two percent? Check the comments on the NYT and see what percentage of readers motivated enough to write a comment got the secret, coded Big Picture message.

75 comments:

Anonymous
said...

Well, when people say 'I can't do math', they mean advanced stuff, not adding 2 + 2, which everyone can do.

This is why 'I'm illiterate' and 'I can't do math' are false comparisons.

After all, most can read and write but few will say they can write sonnets like Shakespeare did or understand Joyce's FINNEGANS WAKE(or master 10 different languages). It is not shameful to say you only know one language or don't get serious literature.

Why does no one in these discussions of math talk about motivation? Math's hard, people have certain IQ's, this kind of teaching might or might not help ... All of that's interesting and important. But what about motivation? Isn't that interesting and important too? If a kid simply doesn't care about math, what're ya gonna do?

I'll surprise no one when I say that I was one such kid. I tested well enough so far as aptitude went, but I had less than zero interest in the subject. Teachers would put me in fast classes and then I'd make it my main life's goal to get out of them. Just couldn't see the sense of anything beyond basic arithmetic for me. And, hey, I've had a nice life anyway.

By the way, no disrespect to math, or to the math-accomplished, intended. I'm very glad that there are people in the world with the drive and talent to take care of the world's math chores and challenges. I just had no desire to be one of them. And, as things have worked out, I've had zero -- and make that ZERO -- reason to put to use any of the trig, geometry and calculus I was subjected to. It was all so much meaningless and useless torture.

Anyway: How are you going to make kids perform well at something when they simply have no interest? Beyond a certain level, math isn't something you can simply hang around and pick up. You really have to apply yourself to it. Some kids might have a decent amount of inborn math talent and horsepower. But if they've got no interest, and if they can't see any decent reason why they should apply themselves, it just ain't gonna happen. This is a big stumbling block (and an underdiscussed one) to the "how are we going to get kids doing better at math?" problem, no?

Hence my conclusion: why force anyone to go past basic arithmetic? Leave the headache-inducing abstract stuff to the kids who really have the desire to manage it. Let the other kids go their own way.

Incidentally, I think some exposure to charts, graphs, and the benefits and perils of statistics is probably a good thing. But all of that can be adequately taken care of with pretty pictures, concrete examples, and plain English.

"Looking at current math achievement levels in the United States, this goal might seem out of reach. But the experience of some educators in Canada and England, using a curriculum called Jump Math, suggests that we seriously underestimate the potential of most students and teachers."

And it raises the question, what is the point of raising these dull students to "university level math" (come off it), if you have to essentially quadruple the teaching hours of instruction given to them? Is that a reasonable trade off? How badly do morons really need to know "university level math"? I mean after all, you don't need to know a lick of math to demand the government give free iPads to surly negroes, or that investing in trillion dollar deficits will "fund" future tax revenues during the next bubble.

At first I thought you meant to write "soft bigotry of high standards", which I would amend to "the soft bigotry of standards"; I see you mean tracking.

So much of our near-term future depends on whether or not we can bring our elites to something like reason regarding Disparate Impact.

In warfare they say to leave your enemy with a means of escape, rather than fighting a desperate foe to his death. Well, "racism" is worse than death, so our elite will have to be provided something other than the truth as a means of escape.

If the truth is heresy we must recourse to hypocrisy. Here's to it. Without hypocrisy civilization wouldn't be possible.

Still, I think we should just plug every manner of thusly implicated virtues into the "soft bigotry of..." trope: excellence, order, enlightenment, etc.

Right, a lot of Americans seem to lack basic mathematical aptitude. In particular, very few people understand concepts like mean, median, variance, etc. That's why we need to keep importing the cognitive elite from East Asia.

Everybody who wants to blather about math education should first shepherd a couple of their kids through elementary and middle school math. Or be one of those kids. Shockingly, this applies as much to op-ed eggheads and Deep Thinkers as to barflies.

We're doing Times Tables these days. If you want to learn multiplication and division, there's no getting around them.

Times Tables. From memory. By rote. Forwards and backwards.

Um, how do I put this nicely to Mister Bornstein? (1) Times Tables are boring, to learn and to teach. (2) Mastery takes discipline and effort. (3) Different kids are different. They pick this stuff up at different rates.

Rocket science, this is not.

If Mister Bornstein and his fellow Great And Good pontificators could force themselves to think clearly about these simple points, they'd have some Aha! moments when reading Sailer and Murray.

Except for cognitive dissonance. Which is a lot harder to tackle than Times Tables.

(1) Times Tables are boring, to learn and to teach. (2) Mastery takes discipline and effort. (3) Different kids are different. They pick this stuff up at different rates.

(4) Mechanical arithmetic can also be done by calculators.

(5) Arithmetic is pretty much devoid of mathematical concepts needed for higher maths. While technically a branch of mathematics, arithmetic requires a different skill set largely irrelevant to anything higher.

It is not uncommon for mathematicians, scientists, and engineers to work out a differential equation in their heads - yet require a calculator to balance their checkbooks.

Rocket science, this is not.

True math, this is not.New math, this is not.

Indeed that is one of the lessons that the public should have learned from New Math in the 1960s.

One irony is that professional mathematicians often jokingly tell their classes or colleagues that they "can't do arithmetic" whenever some calculation arises. The subtext is that they don't consider mental computation very impressive, and that their real talent is in much higher levels of abstraction.

It would be nice if liberals could pass Reality 101 and Honesty 101 for a change.

This JUMP MATH sounds like the sort of thing that led to the NEW ECONOMY--in the late 90s when everyone with dot.com stocks was gonna be a millionaire--and OWNERSHIP SOCIETY where Wall Street, top economists, and politicians of both parties came up with a way to make everyone happy--for bankers to make more money and for every deadbeat to own a home, for free marketeers to beam with pride at the success of capitalism and for socialists to beam with pride with equality in loans. When the going was good, everyone took credit; when things got bad, everyone blamed the 'other guy'.

I remember in the 7th grade one day, for no real reason at all, the math teacher taught us all about the Mobius strip -- but all we learned was a set of curious facts about it, not what it was relevant to or what its properties meant about anything in serious math. The next day we were on to some other random topic, and it was like the Mobius strip would never be mentioned again. This happened repeatedly with all sorts of math concepts that weren't immediately related to arithmetic, trig or early algebra.

No wonder nobody gave a shit, myself included.

I also recall that lots of the thuggish, ostensibly dumb white kids (this was in Brooklyn) who got D's in math nevertheless knew all about baseball and football stats and standings, and understood complicated betting concepts, basic probability, and the arithmetic of giving odds, because they played the football sheets and gambled in the schoolyard. Me, I got A's in math despite not caring about it, but nevertheless I couldn't really understand the math of sports or gambling because I also didn't give a shit about sports and gambling.

All I really wanted was to be left alone to read big books and play the piano, but I understood that the only way I'd be allowed to leave my annoying environment and be left alone, was to get A's in math, about which I did not give the slightest toasty modern shit.

"Take the example of positive and negative integers, which confuse many kids. Given a seemingly straightforward question like, 'What is -7 + 5?', many will end up guessing. One way to break it down, explains Mighton, would be to say: 'Imagine you’re playing a game for money and you lost seven dollars and gained five. Don’t give me a number. Just tell me: Is that a good day or a bad day?'”

Brilliant!! Henceforth, explain E = MC2 by telling students to imagine what what might happen if an ounce of bling was multiplied by the speed of superhero Flash times itself. Or just tell the kids, 'it be da bomb!'

As it happens I was reading some articles by La Griffe du Lion today on ability testing. He focuses on sex differences in math learning rather than bright versus dull, but some of his observations are relevant.

He notes that the sex gap is large. There are more than twice as many men who score above 750 on the quantitative section of the SAT than women. Women outscore men in reading and English but trail men in math and science.

This math gap doesn't show up until puberty. Prior to puberty girls are at least as good at math as boys. That shot of testosterone boys get as a teenager makes them taller, stronger, hairier, and better at math.

The kind of comforting educational reforms espoused here simply can't account for the naked facts. Feminists never seem very concerned that women outscore men in verbal areas, but are outraged that men outscore women in quantitative areas.

I taught math for several years at the graduate and undergraduate levels and I wrote a fair amount of software to teach math. Bornstein and Mighton strike me as charlatans trading on the insecurities of parents.

My advice: get rid of the goddamn government schools, and let the smart kids educate themselves with help from the Web, libraries, and tutors.

This brings up the issue of the shockingly bad instruction we generally get in our public secondary schools. In middle school and high school the "instruction" I received in algebra, trig, and calc (especially calc) was worthless. I aced those courses mostly by memorizing and regurgitating the formulas for exams and homework. It wasn't until I got to university that I finally found good instructors who could actually explain the mathematical concepts clearly and cogently. It would have made high school so much easier and enjoyable if my teachers could have done the same thing. Seriously, most halfway intelligent kids would be better off with just a few good basic textbooks and the Khan Academy videos.

I once had to tutor a kid in pre-calc. He just wasn't getting it. He seemed to be just guessing. I slowly peeled back the layers of his confusion and finally realized he had never mastered fractions. The whole multiplying and dividing by fractions was lost on him -- how could multiplying something make it smaller? Or dividing make it bigger? He should have learned that in at least junior high, if not late grade school. Yet he'd made it through high school as a B student in math without ever really grokking fractions.

"My advice: get rid of the goddamn government schools, and let the smart kids educate themselves with help from the Web, libraries, and tutors."

E.O. Wilson recommended something like the Eagle scouts do. They find out what interests them and go off and research and try to learn. Then they can come for help when they have questions. You can do this with the top students. However you define top.

re: "This brings up the issue of the shockingly bad instruction we generally get in our public secondary schools. In middle school and high school the "instruction" I received in algebra, trig, and calc (especially calc) was worthless."ANON

I was in High School during the 2nd half of the 1950s. Tracking was used without shame. I went to an Honor type of school that does not exist any longer being male only and drawing students from a wide area mostly far from their homes which in my case took about two hours of commuting by public transportation daily.

At any rate, math was taught as it had been for centuries in most of the civilized world before Progressive Education brought the plague of faddism to American Education.

We learned Algebra I & 2, Geometry, Trig., Solid Geometry, Analytical Geometry as had countless souls over centuries doing problems. Yes, problem after problem with about 25 to 30 a day usually 5 days a week during the school year. Lectures were brief and intermittent so, except for periodic tests, most class time was doing problems and those not done were done at home. If a student did not keep up the student would flunk out of school. No one repeated a grade that I can recall and one class flunk was termination. We started with over 600 in 9th grade and graduated less than 300 with most of the washouts being academic losses rather than disciplinary ones.

It worked for me as I ended up in the Ivy League and many, many of my classmates did well academically and were successful in life as High School gave us a foundation to do University level work with ease.

The "wheel" of math education does not need reinventing or math teaching need more fads. Bring back the old methods of DRILL and more DRILL. Lucky for parents this method can be done by home schooling or home supplementation.

One important caveat: Drill is BORING and HARD. When I went through it FEAR of flunking was the motivation. How to motivate a student today is the big question each parent must face. I can not see government schools motivating the students or returning to this method and as such the brighter students will have to do it without government schools.

Isnt the race gap just yet again the reason why this sensible hypocrisy hasnt survived in the past? I mean, if this sensible hypocrisy is applied correctly (ie, not screwing the smart kids) it requires tracking and then you get the racial disparities.

I would hazard a guess that's where most students go off the rails. Math takes practice and review between terms and who does that? And I guess math is "boring" because it's not about people or things necessarily, but it can be fun if, per Tiger Mom, you get good at it and consistently ace the tests.

How so many apparently educated people (they can at least write a grammatically coherent comment) can hold such obviously naive, uninformed, and magical thinking views is appaling. No doubt many are lawyers, teachers, judges, doctors and other upper middle class types.

Even more depressing, is how many commentators use their comment as an emotional enema to salve their bruised egos of "not getting math". They seem to latching onto crap like this redirect their internal shortcomings to external factors (teaching). Such whiney and unfounded self-justification.

One even senses a pride in their mathematical ignorance. Some crow with a misplaced confidence that if only they were spoon-fed babysteps the appropriate size, they would've been the equal of anyone and their math genius know no bounds.

It's sad really. The one good thing about math is that it is pure and undeniably harsh in measuring eveyone's intellectual capacity in black and white.

The most imporant lesson these overopininated and underwhelming NYT readers could get from math is intellectual honesty and humility. No chance of that happening.

"That’s because we think of math ability as something we’re born with, as if there’s a “math gene” that you either inherit or you don’t."

This is a perfect example of a writer citing a pseudo-hatefact as if it's the conventional wisdom, then "bravely" taking a stand against it to espouse egalitarian dogma. Have you come up with a name for this yet Steve?

Teachers tell me that when they begin using Jump they are surprised to discover that what they were teaching as one step may contain as many as seven micro steps.Off course they are!

BF Skinner had this figured out 50 years ago, he was just ahead of his time technology-wise.In 1954 B.F. Skinner embarked upon a series of studies designed to improve teaching methods for spelling, math, and other school subjects by using a mechanical device that would surpass the usual classroom experience. He believed the classroom had disadvantages because the rate of learning for different students was variable and reinforcement was also delayed due to the lack of individual attention. Since personal tutors for every student was usually unavailable, Skinner developed a theory of programmed learning that was to be implemented by teaching machines.http://www.bfskinner.org/BFSkinner/AboutSkinner.html

Tracking is so unfair. Anybody would think life was some sort of competition where people had to compete for jobs and wages were different for different kinds of jobs. Since we know this is obviously not the case in the socialist paradise we live in why should we possibly compare students with one another and crush their self-esteem by telling their parents about how they are doing relative to others.

JSM said..."(4) Mechanical arithmetic can also be done by calculators."

PPPPPTTT. If you don't know your math facts by heart,

The math facts required for arithmetic are very different than the ones required for geometry, algebra, trigonometry, calculus, topology, probability, and statistics.

All these higher maths require arithmetic, but that could still be done by calculator. I often do see scientists and engineers work out complex formulas in their heads or on a sheet of paper, but use a calculator for number crunching, thus avoiding critical mistakes. They quite wisely use their brainpower for the conceptual work unreachable by computers.

Very few mathematicians are good arithmeticians, and vice versa.

which only comes from tedious repetition, factoring quadratic equations will be too frustrating.

There are no concepts involved in arithmetic. Just simple rules and their tedious application.

Giving elementary kids calculators is deliberate sabotage of their education and ought to be punishable by jailtime.

No it isn't.

I can see limiting the use of calculators until the students gain some arithmetical proficiency. But to close the door of higher math to those unable to multiply 204,294 by 92,283,290 in their heads, as some educrats might do, is a crime against humanity.

I already heard the same criticism from the old fogies of the Archie Bunker / Joe Curran generation about kids and those newfangled calculators - and your argument is no different or better.

Engineers and accountants - both heavy number crunching professions - have praised calculators and portable computers to high heaven, for reducing costly arithmetic error.

I had almost exactly the same response that you had to the math article. Tracking FTW. And, Having been in programming and education (math, programming, sports, etc.) for 20 years, I've been working on the math software that you're talking about for a few years now. If I get it to decent working condition, I'll ping you with a url.

What's the difference between Jump and Kumon, which requires lots of rote learning and repetitive exercise to drill in the basics?

(I hope the answer's 'cheapness'. Kumon instruction is £50 a month for a child in the UK, of which the Kumon org. takes 40%. So an instructor with 50 kids attending weekly class and marking the daily papers gets £1500 before expenses. Not exactly riches)

I remember in the 7th grade one day, for no real reason at all, the math teacher taught us all about the Mobius strip -- but all we learned was a set of curious facts about it, not what it was relevant to or what its properties meant about anything in serious math. The next day we were on to some other random topic, and it was like the Mobius strip would never be mentioned again. This happened repeatedly with all sorts of math concepts that weren't immediately related to arithmetic, trig or early algebra.

Educationists call this technique "spiraling" and it's supposed to make math "fun" and "surprising". In actuality, it just makes the subject incoherent and the concepts much harder to remember or use.

This is what happens when you let teachers major in "education" instead of requiring them to major in math, chemistry, and other real subjects.

"If academic performance was the only thing used to track too many white kids would end up of majority black/Hispanic classes and the white parents would be furious"

Right. That's what makes fleeing to an all-affluent district preferable for parents over tracking or examination-entrance schools. Say, you've got two daughters, the older is 110 IQ, the younger 90. The older one gets tracked into the mostly white/Asian track. The younger one gets tracked into the mostly NAM track. That's okay with you ... until puberty when your dumber daughter starts developing crushes on boys in her track. Now, you've got a real problem.

"a lot of Americans seem to lack basic mathematical aptitude. In particular, very few people understand concepts like mean, median, variance, etc. That's why we need to keep importing the cognitive elite from East Asia."

The Housing Bubble is perhaps the best indicator that a whole bunch of Americans lack basic math aptitude, including the president of the US. It was clear, even in 2001 California, that if most above average wage earners couldn't afford to buy the average house, there would eventually be a lot of empty houses. Giving them mortgages they couldn't keep up with over the long term would lead to more foreclosures, not more homeownership.

"Despite the widespread support for “problem-based” or “discovery-based” learning, studies indicate that current teaching approaches underestimate the amount of explicit guidance, “scaffolding” and practice children need to consolidate new concepts."

Jump Math dogma asserting that adding intermediate steps puts a slow kids math understanding on more solid ground is false. In effect, you are simply leading the slow kid through the problem without him grasping the big picture. But once the pedagogical props are kicked out from under the student, he drops back into a ground state of confusion.

For example, if a chapter deals only with multiplication and division by two, after a while the kid will stop reading the problems. He'll look at problem data and double it or divide. A wrong answer likely means the problems have switched from one operation to the other. But once problems require three or more pieces of data and two or more operations, demonstrating full mastery of word problems, the kid will become hopelessly bolluxed up. As a volunteer in my kid's elementary school classroom, I've seen it for myself.

"In every math class I’ve taken, there have been slow kids, average kids and whiz kids. It never occurred to me that this hierarchy might be avoidable."

Doesn't the fine grain approach to teaching math put the lie to Malcolm Gladwell's 10,000 hours countdown-to-mastery twaddle? The new math pedagogy clearly admits that some kids (which rhymes with dumb kids) need to work longer to learn the same stuff as the typical kid, who must work longer to get the same thing as the whiz kid.

Funny how otherwise intelligent people weigh in with "I hate math" as if that's relevant somehow. Math is there, it's required for Physics and other science courses. The worst thing a parent can is sympathize and say is "I was bad at math too - " Hoo boy that's the end of it for most kids.

"That's okay with you ... until puberty when your dumber daughter starts developing crushes on boys in her track. Now, you've got a real problem."

The less likely scenario. The more likely scenario is that when your daughter reaches puberty, she gets sexually harassed or gang raped by Mestizo and Negro youths. Or beat up by a girl gang, where the term girl is somewhat academic, since female hoodies usually have elevated testosterone levels making them capable of masculine savagery.

I should add, there's nothing inherently wrong with pegging the meter.

The narrow hump is not at the low 80-something percentile where you could argue the smart kids are being short-changed. Everybody is doing better than they were before (at least for this modern cohort, like I said I'd like to know how they stack up against historical norms). Hopefully with time and external vigilance by those that know better the tests will get re-normed the other way.

So, if these instructional methods get phenomenal results, by all means let's have more of them. Certainly students are going to hit their mental limit at some point, but if they are highly proficient at everything until hitting their limit, that is a good thing.

"But to close the door of higher math to those unable to multiply 204,294 by 92,283,290 in their heads"Who said anything about doing that problem in their heads? You're just setting up a ridiculous strawman. Doing it by pencil and paper, where you know to start with 4 X 0 = 0; write down the zero; then 4 X 9 = 36, so write down the 6, carry the 3; multiple 4 X 2 = 8 and then add the 3 = 11, so write down a 1 and carry a 1....is an absolutely necessary skill, so THAT the higher maths are comprehensible. Doing such problems develops "number sense," i.e., logical thinking.

*I* am worried about kids in 6th grade who don't instantly know that 4 X 9 = 36 or that 4 X 2 + 3 = 11.THOSE are the kids that are going to find it impossible to think of a combination of digits that, say, adds up to 11 and multiplies to 24.

But if a kid knows his arithmetic math facts by heart, the required combination of digits (3 and 8) is immediately apparent.

Which means factoring quadratic equations will be too much frustration, which means you'll be stalling out in Algebra 1.

I've seen PLENTY of smart kids who struggle in Algebra 1 simply because they have not memorized their math facts, because their teachers gave them calculators in elementary school, so they didn't have to.

"Engineers and accountants - both heavy number crunching professions - have praised calculators and portable computers to high heaven, for reducing costly arithmetic error."

Your argument, that because very, very smart people often use calculators to save themselves some work they find tedious --work which they fully UNDERSTAND how to do, btw -- that that means elem school kids should just rely on calculators...

...reminds me of the fool-headed arguments back when "whole language" was all the rage for "teaching" reading. Argument went like this: gifted children often learn to read without any direct, specific instruction from anybody; they just seem to figure it out for themselves.So, "EUREKA! Let's not bother to teach phonics to average kids. Just give them good books and they'll figure it out for themselves! What could go wrong?"

The whole language fad left an entire generation nearly functionally illiterate. Why? Because average people are not gifted, duh. Average people need systematic, step-by-step, thorough, direct instruction in the basics, accompanied by lots and lots of repetition, and THEN they'll "get it." Without it, they are helpless.Give an average kid a calculator in grade school so he doesn't have to strain himself to memorize his math facts, he'll LOVE you for it. And YOU'll have CRIPPLED him.

Maybe this latest educational fad of babystep-by-babystep will force teachers to start teaching math in a methodical and coherent fashion, in which case it might be a distinct improvement over the fluffy shenanigans they've been using for the last few decades. But given the low quality of most teachers to begin with (not to mention the low quality of most NAM students), I wouldn't get my hopes up.

My point in my earlier comment was that if you aren't interested in math, you'll never be good at it. Simple as that. (On aptitude tests, I scored as well as friends who went on to be scientists, engineers and doctors. But I had no use for any of that.)

It isn't a mechanical problem. It's at least partly a human one. Aptitude doesn't equal achievement. You gotta have desire and determination too. And where do those come from?

A pretty good summary of the horrors of attending overwhelmingly NAM schools:

(prev. thread) AmericanGoy: I went to a majority black high school for first 2 years...a mob of black kids WILL pick on the lone white kid, no ifs or buts about it..A black security guard saved my life (no kidding)..I viewed the experience like a prison with very lax security...The emphasis was on not getting into trouble, and I cannot remember learning anything other than to look around a lot..

(prev. thread) Wandrin: If you're White in a very minority White school then you'll get attacked all the time...Mine was all boys but my sister's was mixed and there was also a huge amount of sexual assault and the occasional gang rape on top of the standard violence...Luckily i didn't need to but i would have killed and robbed people if it was the only way to avoid my kids going to a school like that.

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Fourth: if you have a Wells Fargo bank account, you can transfer money to me (with no fees) via Wells Fargo SurePay. Just tell WF SurePay to send the money to my ancient AOL email address steveslrATaol.com -- replace the AT with the usual @). (Non-tax deductible.)

Fifth: if you have a Chase bank account (or, theoretically,other bank accounts), you can transfer money to me (with no fees) via Chase QuickPay (FAQ). Just tell Chase QuickPay to send the money to my ancient AOL email address (steveslrATaol.com -- replace the AT with the usual @). If Chase asks for the name on my account, it's Steven Sailer with an n at the end of Steven. (Non-tax deductible.)

My Book:

"Steve Sailer gives us the real Barack Obama, who turns out to be very, very different - and much more interesting - than the bland healer/uniter image stitched together out of whole cloth this past six years by Obama's packager, David Axelrod. Making heavy use of Obama's own writings, which he admires for their literary artistry, Sailer gives the deepest insights I have yet seen into Obama's lifelong obsession with 'race and inheritance,' and rounds off his brilliant character portrait with speculations on how Obama's personality might play out in the Presidency." - John Derbyshire Author, "Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics" Click on the image above to buy my book, a reader's guide to the new President's autobiography.